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Finding the Fourth Proportional to 405.86, 609.10 and 314.34

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Solution

The fourth proportional to 405.86, 609.10 and 314.34 is: 471.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    405.86 : 609.10 = 314.34 : x
  2. Step 2: Convert to fraction form
    405.86/609.10 = 314.34/x
  3. Step 3: Cross multiply
    405.86x = 609.10 × 314.34
  4. Step 4: Simplify right side
    405.86x = 191,464.49
  5. Step 5: Solve for x
    x = 191,464.49/405.86
  6. Step 6: Final answer
    x = 471.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.